Difference between revisions of "Template:Free surface dock relations"

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== Inner product between free surface and dock modes ==
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=== Inner product between free surface and dock modes ===
  
 
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Revision as of 04:21, 23 September 2008

Inner product between free surface and dock modes

[math]\displaystyle{ \int\nolimits_{-h}^{0}\phi_{n}(z)\psi_{m}(z) d z=B_{mn} }[/math]

where

[math]\displaystyle{ B_{mn}=\frac{k_{n}\sin k_{n}h\cos\kappa_{m}h-\kappa_{m}\cos k_{n}h\sin \kappa_{m}h}{\left( \cos k_{n}h\right) \left( k_{n} ^{2}-\kappa_{m}^{2}\right) } }[/math]